Systems for monitoring acoustic vibration in a borehole in an earth formation such as in the downhole completion and carbon dioxide sequestration industries have been employed. However, typical systems rely on Rayleigh backscatter. This approach allows for measurements over a very long distance at acceptably high sampling frequencies, which works fine for applications such as leak detection where it is desirable to monitor a long length of an installation. However, the sensitivity of this approach is limited due to the fact that only a very small portion of the transmitted radiation is reflected by Rayleigh backscatter. This makes the approach less desirable in applications where a more sensitive measurement is needed. The industry is receptive to systems and methods that overcome the foregoing limitations while allowing more precise monitoring of a particular component.